Question: Rewrite as a simplified fraction. ${3.\overline{65} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 365.6565...\\ 1x &= 3.6565...\end{align*}}$ Subtracting the two equations, we have: ${99x = 362}$ ${x = \dfrac{362}{99}} \text{or} {3 \dfrac{65}{99}}$